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Between April and September 2011, 6.5 million customers waited more than ten minutes to have their call answered.

The NAO was especially critical because customers are charged premium rates as soon as that their calls are connected, even if they are held in a queue.

The NAO estimated that customers paid £33 million in call charges while they are in the queue, while the estimated value of customers’ time was £103 million.

It is likely that HMRC’s performance was exaggerated because customers who hung up during the automated message were counted as being answered.

The watchdog found that nearly a third of the 15million callers who HMRC assumed had been satisfied by an automated message called back within 24 hours.

This suggested that they were frustrated at having to listen to the message, and had decided to call back at a later date.

Margaret Hodge, the chairman of the Public Accounts Committee which oversees the work of the NAO, said taxpayers were getting a “substandard” performance.

She said: “HMRC needs to be far more ambitious in its efforts to improve the customer service it currently provides.

“Targets must better match those of other organisations to greatly reduce the time callers are left hanging on the line and it needs to provide alternatives to 0845 numbers.

“Customer service at HMRC has been too poor for too long. It needs to put in place a formal strategy for how it is going to make long term service improvements that centre on the needs of customers.”

Mrs Hodge said it was “totally unacceptable that HMRC uses costly 0845 numbers and charges people for the privilege of waiting for the Department to pick up”.

An HMRC spokesman said: "By late 2012 we were answering over 90 per cent of calls to our contact centres but we are well aware that in the past we have not delivered the standard of service to which we are committed.

"We are determined to build on this progress and we have invested £34 million so we can deliver on our improvement targets earlier than planned.

"We receive well over 10 million pieces of post every year, and the most recent figures show we are now replying to over 80% within 15 working days.

“We want people to be able to access our phone services at the lowest possible cost to them, whilst ensuring value for money to the taxpayer. As part of this commitment we have transferred our Tax Credits Phone Lines, accounting for around 40% of our calls, from 0845 to 0345 numbers.

"We are determined to build on these improvements until we deliver the quality of service to which our customers are entitled to expect."